//
//---------------------  1D  ---------------------
//
//
// Quick is not defined for 1D
//

//
//---------------------  2D  ---------------------
//
//       Staggered Mesh for u-vel and v-vel
//
//   0       1       2       3       4       5   
//
//5      >       >       >       >       > 
//       |       |       |       |       |              
//   ^---+---^---+---^---+---^---+---^---+---^  4       Mesh for scalar fields
//       |       |       |       |       | 
//4      >   o   >   o   >   o   >   o   >               5  x-x-+-x-+-x-+-x-x
//       |       |       |       |       |               4  x o | o | o | o x
//   ^---+---^---+---^---+---^---+---^---+---^  3           +---+---+---+---+
//       |       |       |       |       |               3  x o | o | o | o x
//3      >   o   >   o   >   o   >   o   >                  +---+---+---+---+
//       |       |       |       |       |               2  x o | o | o | o x
//   ^---+---^---+---^---+---^---+---^---+---^  2           +---+---+---+---+
//       |       |       |       |       |               1  x o | o | o | o x
//2      >   o   >   o   >   o   >   o   >               0  x-x-+-x-+-x-+-x-x
//       |       |       |       |       |                  
//   ^---+---^---+---^---+---^---+---^---+---^  1           0 1   2   3   4 5 
//       |       |       |       |       |                 
//1      >   o   >   o   >   o   >   o   >                 o central node
//       |       |       |       |       |                 x boundary node
//   ^---+---^---+---^---+---^---+---^---+---^  0          > u velocity 
//       |       |       |       |       |                 ^ v velocity
//0      >       >       >       >       >    
//       0       1       2       3       4             
//
//                                                  
//          Volumes for v-velocity
//
//       0       1       2       3       4       
//
//       >       >       >       >       >      5
//       :       :       :       :       :              
//4  ^...+---^---+---^---+---^---+---^---+...^          Mesh for scalar fields
//       |       |       |       |       | 
//       >---o--->---o--->---o--->---o--->      4        5  x-x-+-x-+-x-+-x-x
//       |       |       |       |       |               4  x o | o | o | o x
//3  ^...+...^...+...^...+...^...+...^...+...^              +---+---+---+---+
//       |       |       |       |       |               3  x o | o | o | o x
//       >---o--->---o--->---o--->---o--->      3           +---+---+---+---+
//       |       |       |       |       |               2  x o | o | o | o x
//2  ^...+...^...+...^...+...^...+...^...+...^              +---+---+---+---+
//       |       |       |       |       |               1  x o | o | o | o x
//       >---o--->---o--->---o--->---o--->      2        0  x-x-+-x-+-x-+-x-x
//       |       |       |       |       |                  
//1  ^...+...^...+...^...+...^...+...^...+...^              0 1   2   3   4 5 
//       |       |       |       |       |                 
//       >---o--->---o--->---o--->---o--->      1          o central node
//       |       |       |       |       |                 x boundary node
//0  ^...+---^---+---^---+---^---+---^---+...^             > u velocity 
//       :       :       :       :       :                 ^ v velocity
//       >       >       >       >       >      0
//
//   0       1       2       3       4       5             
//
//                       
//                  |           |           |           |
//                -->-----o----->-----o----->-----o----->-- 
//                  |     :     |     :     |     :     |               
//                  |     :     |  (i,j+1)  |     :     |
//                  |     ^     |    v_N    |     ^     |   
//                  |     :     |     :     |     :     |
//                  |     :     |     :     |     :     |
//                -->-----o---- 3 -- v_n -- 4 ----o----->--  4 = u(i  , j+1)
//                  |     :     |     :     |     :     |    3 = u(i-1, j+1)
//                  |     :     |     :     |     :     |    2 = u(i  , j  )
//                  |    v_W   u_w   v_P   u_e   v_E    |    1 = u(i-1, j  )
//                  |  (i-1,j)  |   (i,j)   |  (i+1,j)  |
//                  |     :     |     :     |     :     |
//                -->-----o---- 1 -- v_s -- 2 ----o----->-- 
//                  |     :     |     :     |     :     |               
//                  |     :     |     :     |     :     |
//                  |     ^     |    v_S    |     ^     |   
//                  |     :     |  (i,j-1)  |     :     |
//                  |     :     |     :     |     :     |
//                -->-----o----->-----o----->-----o----->--
//                  |           |           |           | 
//                  
//               1           3                       2         4 
//   u_w = ( u(i-1,j) + u(i-1,j+1) ) / 2   u_e = ( u(i,j) + u(i,j+1) ) / 2
//   v_n = ( v(i,j) + v(i,j+1) ) / 2     v_s = ( v(i,j) + v(i,j-1) ) / 2
//               

namespace Tuna {

template<class T_number, int Dim>
inline bool Quick_YCoDi<T_number, Dim>::calcCoefficients2D() 
{
    prec_t dy_dx = Gamma * dy / dx;
    prec_t dx_dy = Gamma * dx / dy;
    prec_t dxy_dt = dx * dy / dt;
    prec_t RaGaVol = Rayleigh * Gamma * 0.5 * dx * dy;
    prec_t ce, cem, cep, cw, cwm, cwp;
    prec_t cn, cnm, cnp, cs, csm, csp;
    aE = 0.0; aW = 0.0; aN = 0.0; aS = 0.0; aP = 0.0; 
    sp = 0.0;

    for (int i =  bi; i <= ei; ++i)
	for (int j = bj; j <= ej; ++j)
	{
	    ce = ( u(i,j) + u(i,j+1) ) * 0.5 * dy;
	    cw = ( u(i-1,j) + u(i-1,j+1) ) * 0.5 * dy;
	    cn = ( v(i,j) + v(i,j+1) ) * 0.5 * dx;
	    cs = ( v(i,j) + v(i,j-1) ) * 0.5 * dx;

	    if ( ce > 0 ) { cem = 0.0; cep = ce * 0.125; }
	    else {          cem = -ce * 0.125; cep = 0.0; }
	    
	    if ( cw > 0 ) { cwm = 0.0; cwp = cw * 0.125; }
	    else {          cwm = -cw * 0.125; cwp = 0.0; }

	    if ( cn > 0 ) { cnm = 0.0; cnp = cn * 0.125; }
	    else {          cnm = -cn * 0.125; cnp = 0.0; }
		
	    if ( cs > 0 ) { csm = 0.0; csp = cs * 0.125; }
	    else {          csm = -cs * 0.125; csp = 0.0; }

	    aE (i,j) = dy_dx - ce * 0.5 + cep - 2 * cem - cwm;
	    aW (i,j) = dy_dx + cw * 0.5 + 2 * cwp - cwm + cep; 
	    aN (i,j) = dx_dy - cn * 0.5 + cnp - 2 * cnm - csm;
	    aS (i,j) = dx_dy + cs * 0.5 + 2 * csp - csm + cnp; 
	    aP (i,j) = aE (i,j) + aW (i,j) + aN (i,j) + aS (i,j) + dxy_dt +
			cem - cwp + cnm - csp;
//			+ (ce - cw) + (cn - cs);
// Term (ce - cw) is part of discretizated continuity equation, and
// must be equal to zero when that equation is valid, so I can avoid
// this term for efficiency.

	    sp (i,j) = v(i,j) * dxy_dt - ( p(i,j+1) - p(i,j) ) * dx +
	      RaGaVol * ( T(i,j) + T(i,j+1) );
	    
	    if (i <= ei-1)        { sp (i,j) += cem * v(i+2,j); }
	    else if ( i == ei) { sp (i,j) += cem * v(i+1,j); }

	    if (i >= bi+1)        { sp (i,j) -= cwp * v(i-2,j); }
	    else if ( i == bi) { sp (i,j) -= cwp * v(i-1,j); }

	    if (j <= ej-1)        { sp (i,j) += cnm * v(i,j+2); }
	    else if ( j == ej) { sp (i,j) += cnm * v(i,j+1); }

	    if (j >= bj+1)        { sp (i,j) -= csp * v(i,j-2); }
	    else if ( j == bj) { sp (i,j) -= csp * v(i,j-1); }

	}   
    calc_dv_2D();
    applyBoundaryConditions2D();
    return 0;     
}

//
//---------------------  3D  ---------------------
//
template<class T_number, int Dim>
inline bool Quick_YCoDi<T_number, Dim>::calcCoefficients3D() 
{
    prec_t dyz = dy * dz, dyz_dx = Gamma * dyz / dx;
    prec_t dxz = dx * dz, dxz_dy = Gamma * dxz / dy;
    prec_t dxy = dx * dy, dxy_dz = Gamma * dxy / dz;
    prec_t dxyz_dt = dx * dy * dz / dt;
    prec_t RaGaVol = Rayleigh * Gamma * 0.5 * dx * dy * dz;
    prec_t ce, cem, cep, cw, cwm, cwp;
    prec_t cn, cnm, cnp, cs, csm, csp;
    prec_t cf, cfm, cfp, cb, cbm, cbp;
    aE = 0.0; aW = 0.0; aN = 0.0; aS = 0.0; aF = 0.0; aB = 0.0; aP = 0.0; 
    sp = 0.0;

    for (int k = bk; k <= ek; ++k)
    	for (int i =  bi; i <= ei; ++i)
	    for (int j = bj; j <= ej; ++j)
	    {
		ce = ( u(i,j,k) + u(i,j+1,k) ) * 0.5 * dyz;
		cw = ( u(i-1,j,k) + u(i-1,j+1,k) ) * 0.5 * dyz;
		cn = ( v(i,j,k) + v(i,j+1,k) ) * 0.5 * dxz;
		cs = ( v(i,j,k) + v(i,j-1,k) ) * 0.5 * dxz;
		cf = ( w(i,j,k) + w(i,j,k+1) ) * 0.5 * dxy;
		cb = ( w(i-1,j,k) + w(i-1,j,k+1) ) * 0.5 * dxy;

		if ( ce > 0 ) { cem = 0.0; cep = ce * 0.125; }
		else {          cem = -ce * 0.125; cep = 0.0; }
		
		if ( cw > 0 ) { cwm = 0.0; cwp = cw * 0.125; }
		else {          cwm = -cw * 0.125; cwp = 0.0; }

		if ( cn > 0 ) { cnm = 0.0; cnp = cn * 0.125; }
		else {          cnm = -cn * 0.125; cnp = 0.0; }
		
		if ( cs > 0 ) { csm = 0.0; csp = cs * 0.125; }
		else {          csm = -cs * 0.125; csp = 0.0; }

		if ( cf > 0 ) { cfm = 0.0; cfp = cf * 0.125; }
		else {          cfm = -cf * 0.125; cfp = 0.0; }
		
		if ( cb > 0 ) { cbm = 0.0; cbp = cb * 0.125; }
		else {          cbm = -cb * 0.125; cbp = 0.0; }		

		aE (i,j,k) = dyz_dx - ce * 0.5 + cep - 2 * cem - cwm;
		aW (i,j,k) = dyz_dx + cw * 0.5 + 2 * cwp - cwm + cep; 
		aN (i,j,k) = dxz_dy - cn * 0.5 + cnp - 2 * cnm - csm;
		aS (i,j,k) = dxz_dy + cs * 0.5 + 2 * csp - csm + cnp;
		aF (i,j,k) = dxy_dz - cf * 0.5 + cfp - 2 * cfm - cbm;
		aB (i,j,k) = dxy_dz + cb * 0.5 + 2 * cbp - cbm + cfp; 
		aP (i,j,k) = aE (i,j,k) + aW (i,j,k) + aN (i,j,k) + aS (i,j,k) +
			aF (i,j,k) + aB (i,j,k) +
			cem - cwp + cnm - csp + cfm - cbp + dxyz_dt;
//			+ (ce - cw) + (cn - cs) + (cf - cb);
// Term (ce - cw) is part of discretizated continuity equation, and
// must be equal to zero when that equation is valid, so I can avoid
// this term for efficiency.

		sp (i,j,k) = v(i,j,k) * dxyz_dt - 
		    ( p(i,j+1,k) - p(i,j,k) ) * dxz +
		  RaGaVol * ( T(i,j,k) + T(i,j+1,k) );
	    
		if (i <= ei-1)        { sp (i,j,k) += cem * v(i+2,j,k); }
		else if ( i == ei) { sp (i,j,k) += cem * v(i+1,j,k); }
		
		if (i >= bi+1)        { sp (i,j,k) -= cwp * v(i-2,j,k); }
		else if ( i == bi) { sp (i,j,k) -= cwp * v(i-1,j,k); }

		if (j <= ej-1)        { sp (i,j,k) += cnm * v(i,j+2,k); }
		else if ( j == ej) { sp (i,j,k) += cnm * v(i,j+1,k); }

		if (j >= bj+1)        { sp (i,j,k) -= csp * v(i,j-2,k); }
		else if ( j == bj) { sp (i,j,k) -= csp * v(i,j-1,k); }

		if (k <= ek-1)        { sp (i,j,k) += cfm * v(i,j,k+2); }
		else if ( k == ek) { sp (i,j,k) += cfm * v(i,j,k+1); }
		
		if (k >= bk+1)        { sp (i,j,k) -= cbp * v(i,j,k-2); }
		else if ( k == bk) { sp (i,j,k) -= cbp * v(i,j,k-1); }
	    }
    calc_dv_3D();
    applyBoundaryConditions3D();   
    return 0;
}

} // Tuna namespace















